Question

Show that there does not exist any numbercsuch that the following functionf (x)would be a p.d.f.:

Short answer

There does not exist any number c such that

is a probability density function.

Step-by-step solution

Given the information

The function is given as,

Calculate the value of c 

For a function to be a probability density function, the function should hold the following condition.

\int\limits_x^{}{f\left(x\right)}=1

For the provided function, the calculations are as follows:

Since, In (∞ ) = ∞ and In (0) is not defined, there does not exist any number c such that the provided function is a probability density function.